2025 Paradigm Sec 3 Mock EOY Q4

[Surds]

A cylinder has volume \((\sqrt{45}+\sqrt3)\text{ cm}^3\). If the base area of the cylinder is \((\sqrt{45}-\sqrt3)\text{ cm}^2\), find the height of the cylinder.

Give your answer in the form \(a+b\sqrt{15}\), where \(a\) and \(b\) are rational numbers.[3]